1
DISCRETE MATHEMATICS 1 TEST 1
SPECIMEN
1. (4 pts) How many ways are there to distribute 18 balls among 6 different persons if a) each ball is different and each person should get 3 balls
b) all balls are identical ?
2. (5 pts) Show by combinatorial arguments that:
Xm k=0
m k
! n r + k
!
= m + n m + r
!
.
3. (5 pts) Show that P (n, k) = P (n − 1, k − 1) + P (n − k, k) for each 1 < k < n.
4. (4 pts) How many permutations of the letters a, a, a, b, b, b, c, c, c, d, d, d are there with no three consecutive letters the same?
